Welcome to the forums.
Physicals files names in SQL for default are: .mdf for data files and .ldf for log files.
If SQL is running you can't delete those files. Now if SQL is down, then you can delete those files and, when SQL is up, your database became to suspect and unusable.
About restore question, yes if that database was created with .mdf and .ldf names.

whenever you create a new database you always will have these two files they are know as Data files
the MDF file is the file that contains the data in your database and the LDF file will be the log file
all transactions (Inserts, Deletes and Updates) that you issue against the database are first recorded in the ldf file and then it goes fisically to the MDF

if you delete one of these files you will losse the database and there will be no way to recover it unless you have a database backup

and whenever you restore a backup you are restoring these two files basically